Find x - Show Work.

Question

M is the midpoint of PQ. PM = 5x+8 and PQ = 76, find x.

Answer 1

A picture is very helpful:

 

   P                         M                         Q

   ♦---------------------♦---------------------♦

   |<----  5x+8  ---->|<---- 5x+8 ---->| 

   |<------------------------  76  --------->|

 

 

The "midpoint" is located at half ("mid") of the total distance.

      5x + 8  =  (1/2)76        or    2(5x+8)=76

 

       5x + 8 = 38

       5x =  30                [subtract 8 from both sides]

        x = 6                    [divide both sides by 5]

 

Check:

    Is    5(6)+8 = (1/2)76   ?

               38 = 38   ?yes

Answer 2

 P       5X+8        M                      Q

 

 P                       76                     Q

 

 

The variable X is what 5 needs to be multiplied by and added to 8 to total 76, therefore 

 

5X+8 = 76

     -8    -8

 

The 8 is subtracted from itself as well as the 76 to get the 5X on the left side of the equal sign

 

After subtracting 8 from itself and 76 your problem should like this:

 

5X (8-8) = 68 (76-8)

 

5X = 68

 

Now that the problem has been simplified, we're going to to now get the unknown variable or 'X' by itself then apply it to the initial problem therefore, divide both side with the number that is next to the unknown variable

 

5X = 68 

5       5

 

After performing division on both sides of the problem your result should be 

 

X = 13.6

 

Now, to ensure your answer is correct apply the now known variable, the result of 'X', into the initial equation

 

5 (13.6) + 8 = 76